Analytic Correlation Penalty with Variable Window in Multi-task Learning Disease Progression Model

Alzheimer's Disease (AD) is the most common reason of dementia that causes serious problems in patients' congnitive functions. Multi-task learning (MTL) has performed well in studies of longitudinal processes in Alzheimer's disease for revealing the progression of AD. Combined with prior knowl-edges in disease progression or medical science, regularization MTL framework could introduce empirical constraints more flexibly. Meanwhile, it brings higher cost during optimization. While it shown that most of formulations could not define the disease progression precisely. Existing regression methods with temporal smoothness method eliminated abnormal fluctuation of cognitive scores, and neglected the sophisticated progression in disease. In this article, we proposed an analytic method to define the progression of AD, and a flexible bandwidth method to encourage the points of disease time sequence temporal smoothness in an appropriate way. To solve three non-smooth penalties in our method, we proposed an optimization method combined accelerated gradient descent (AGD) and alternating direction method of multipliers (ADMM).